Wave transmission network



sept.2, 1947. f w, P, MASON 2 2,426,633

WAVE TRANSM S S ION NETWORK l Filed Aug. 12, 1945 A TTENl/ATION A 7` TORNEV latentecl Sept. 2,

OFFICE y WAVE TRANSMISSION Nit'rvvolni Warren I. Mason, West Orange, N. J., assigiior to Bell Telephone Laboratories', Incorporated, New York, N. Y., a corporation of New York Application August 12, 1943, Serial No. 498,325

11 Claims.

This invention relates to wave transmission networks and more particularly to branching circuits comprising a plurality of series-connected Wave iilters made up of sections of coaxial transmission line for combining or separating a plurality of different bands of frequencies.

The principal object of the invention is to place upon a common transmission line simultaneously a plurality of bands of frequencies from different sources or to separate into individual channels a plurality of bands simultaneously transmitted by one line.

Another object is to increase the voltage rating of filters comprising coaxial elements.

Other objects of the invention are to reduce the size and cost and increase the shielding of a series-connected branching circuit.

A branching circuit is required Whenever two or more bands of frequencies from different sources are to be put on one transmission line or when signals on a line are to be separated into individual channels according to frequency. In accordance with the invention the channels of such a branching circuit are connected in series. Each channel is provided with a band-pass lter comprising two sections of coaxial transmission line connected in tandem and one r more sections connected in shunt at their junction. In order to provide a fully shielded compact structure all of the series branches at the connected ends of the filters are arranged concentrically. With this construction the inner conductor of one branch serves as the outer conductor of another branch. In each of the filters except the one o f lowest frequency there is a short-circuited coaxial shunt branch which is arranged in line with the concentric series branch and the other series branch makes a right angle with the concentric series branch. The voltage rating of any of the filters may be increased economically by providing a plurality of coaxial shunt branches of the same length connected in parallel at the same point, thus increasing the separation between the inner and the outer conductors. Also, to simplify the construction, al1 of the coaxial elements of any one lter may be made with outer conductors of the same inner diameter.

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawings in which like reference characters refer to similar or corresponding parts, and in which:

Fig. 1 is a longitudinal cross-section of a twochannel branching circuit in accordance with the invention;

Figs. 2 and 3 show the equivalent electrical circuits for the filters used in the arrangement of Fig. 1; and

Fig. 4 gives typical attenuation-frequency characteristics for the filters.

Fig. 1 shows two band-pass wave filters 4 and 5 connected in series at one end to form a twochannel branching circuit. Each of the filters 4 and 5 is a ladder structure composed of sections of coaxial transmission line. The filter 4 comprises two similar tandem-connected sections of line 6 and l, each of length A, and two identical sections 8 and 9, each of length B, short-circuited at their distant ends by end plates Il and connected in shunt at the junction point I0 of the sections 6 and 1. The section l, for example, consists of an outer cylindrical conductor I2 and coaxial therewith an inner conductor I3. The filter 5 comprises two tandem-connected sections of line I4 and I5, each of length'D, and a single shunt section I6 of length E connected at the junction point I'I and short-circuited at its distant end by the annular plate 31. The sections Iii and I6 are arranged in axial alignment and are concentric with the line section I of the filter d. The Outer conducto-r I2 of the section 'I thus serves as the inner conductor of the sections I4 and I6. The axis of the section I5 makes a right angle with the, axis of the sections IllY and I6. With this construction both mounting space and material are conserved and continuous shielding is provided for the entire branching circuit. In order to save drawing space, in Fig. 1 portions of the line sections 6, 1, 8, 9 and I6 have been removed.

The filter 4 is designed to transmit a band with mid-band frequency of fm1 and the filter 5 a higher band with mid-band frequency fm2. Since the filters are connected in series at their righthand ends, if signals falling within these bands are impressed upon the circuit at the terminals I8, I9, the lower frequency signals may be taken olf at the terminals 20, 2| and the higher frequency signals at the terminals 22, 23 for utilization in separate channels. Alternatively, signals within these bands from separate sources may be impressed upon the terminals 2U, 2| and 22, 23 respectively, and combined in a utilization circuit connected to the terminals I8, I9. These possibilities are indicated by the double pointed arrows and the appropriate mid-band frequencies associated therewith.

The electrical design of the filters will now be considered. It will be assumed that the filter 4 is required to transmit a band of frequencies extending from fn to T21 with a mid-band frequency of fm1, which is the geometric mean of the two, and the lter 5 a higher band between i12 and fzz with a mid-band frequency of fm2. The design may be worked out most conveniently by referring to the equivalent electrical circuit which for the lter Il is shown in Fig. 2. The circuit is a ladder-type netwerk with input terminals 25, `2-6 and output terminals 21, 28. The series inductance LA at the left and the two capacitance's CA, CA connected in shunt at the ends thereof are furnished by the line section E. The series `inductance LA at the right and the two shunt capacitances associated therewith are 'supplied by the line section 1. The central shunt branch made up of the inductance LBand. the capacitance CB connected in parallel represents the two shuntconnected line sections 8 and 9.

The approximate values of these elements in terms of the lengths and characteristic impedances of the line sections are given by the following formulas: Y Y

in which A` and B are the lengths in centimeters of the line sections 6 and 8 respectively, ZA and ZB are respectively their characteristic impedances, n is the number of identical shuntvbranches and V is the velocity of propagation in the sections, which may beY taken as 3 1010 centimeters per second. It is assumed that the series resistanceand distributedconductance of the line sections are small enough to be neglected. In Equation 4 the factor 8/1;2 is used-because the lengthA of section 8 isin the neighborhood ofi-a quarterwavet lengthand is short-circuitedat the end. In this connection reference is made to Equation 2.139 and the accompanying Vdiscussion on page 6 5 of applicants book, Electromechanical Transducers and- Wave Filters, published by D.- VanV Nostrand,Inc. K

The two capa-citances CA, CA connectedv in lshunt at the ends of the circuit Of 2 are usually small enough to be neglected. When this i'smdone, the remaining circuit will be recognized Aas a midseries terminated filter section of the type shown as structure 12 in Table I on pages 52 and 53 of applicants above-mentioned book, the design formulas for which, as applied to Fig. 2, are as follows: f

where Zo isthe image impedance. of the lter at.

the mid-band frequency fm1. v n Y A suggested design procedure 'for the. ll'te'r 4 `will now be presented. The image impedance y'Zo is usually chosen to match the impedance of the loads which are to be connected to the terminals I8, I9 and 2D, 2|. The cut-olf frequencies ,in and ,121 are chosen and the required values of the elements LA, LB and the sum of 2CA and CB are computed from Equations 5, 6 and '7. The length B of each of the shunt branches 8 and 9 is next chosen. This may conveniently be taken as a quarter wavelength at the mid-band frequency in accordance with the formula:

V B '4m The number n of shunt branches that will be required is ordinarily not known at this stage so it may be taken as unity. The impedance ZB of a single shunt branch as thus determined may be multiplied by n to find the impedance of each shunt branch as explained more fully below. Now the value of LB found from Equation 6 and the length B as given by Equation 8 are substituted in Equation 4 to find the characteristic impedance ZB of the shunt branch, assuming that n is unity. Next the value of CB is found from Equation 3. Since the sum of 2CAand CB is known from Equation '7, the value of CA can be found. This value of CA is substituted in Equation 1, the value of LA as found from Equation 5 is substituted in Equation 2 and the two equations solved simultaneously for the required length A and characteristic impedance ZAY of each series branch 6 and l. In a coaxial line the ratio ofy the inner diameter b ofy the outer conductorto the diameter a of the inner conductor is related to the characteristic impedance ZK 0f the line by the formula: Y

ZKGOlog. (9)

The number n of Yshunt branches required depends primar-ily upon the peak voltage that will be impressed upon the lter. VAs an illustrative example, if the nlter ll has. an image impedance Z0 of 50 ohms and is to transmita band lying between 200 and 280 megacycles 'per second each of the branches 6 and i will have a length A of 18.42 centimeters and a characteristic impedance ZA ofv 46.4 oh'ms and a single shunt branch will have a length B of- 31.7 centimeters and a characteristic 'impedance of 15.96 ohms. The outer conductors of the 'series branches 6 andV 'l and the shunt branch may most convenientlyhfave the same inner diameter whichshould not be too large since the higher frequency. filter 5 is to be voltage gradient between inner an'dlout'e'r conductors of the coaxial elements is '10,1000 vous per centi-meter. It -is'apparent--that the single shunt 'blanrch with a separation orV 0,1130 centimetrrwiii Withstndqnly-lgoo VOUS- HOWSVBT; in accorda.

ance withthe invention, this,situation.'mayfbeY remedied by Yir`ic'rea'sing,..th'eY number 'offQsllllit` branches to n and making the charac'teristicimv pedance of each n times the impedance of the single shunt. The length of each of the n branches will be the same as that of the single shunt branch. As shown in Fig. 1, for example, two shunt branches 8 and 9 are used. The characteristic impedance of each will be two times 15.96 or 31.92 ohms. The ratio oi diameters will be 1.702, giving e, diameter of 0.649 for the inner conductor 24 and a separation of 0.229 centimeter. Each shunt branch will withstand 'a voltage of 2,290 volts, which is greater than the assumed peak voltage of 2,000 for the filter. The number of shunt branches may, of course, be increased to more than two, as, for example, to three or four, thus further increasing the voltage rating of the branches. Each of the series branches 6 and 'I will have a ratio of diameters of 2.75, giving a diameter of 0.509 centimeter for the inner conductor and a separation of 0.299 centimeter, which is more than adequate for a voltage of 2,000. Y

The solid line curve of Fig. 4 gives the attenuation-frequency characteristic of the lter 4. The lter has a multiband characteristic with the mid-band frequencies occurring at (2s-1) fm1, where s is an integer. Only the rst three transmission bands with mid-band frequencies of fm1, fm1' and fm1 vare shown. All of these bands have the same width in cycles. It should be pointed out that any one of these bands may be utilized, either the rst extending from fn to fzi, the second from fn to f21, the third from fn" to fzi or a higher one, depen-ding upon the frequency range to be carried by the channel connected to the terminals 20, 2 I.

The electrical design of the lter 5 will now be considered. Fig. 3 gives the equivalent electrical circuit, which is similar to that of the lter 4 given in Fig. 2. The series inductances LD, LD, and their associated shunt capacitances CD, are furnished respectively by the line sections I4 and I5. The shunt branch made up of LE and CE connected in parallel represents the line section I6.

The approximate values of these elements in terms of the lengths and characteristic impedances of the line sections are given by the following formulas:

in which D and E are the lengths in centimeters of the line sections I4 and IB respectively, and ZD and ZE are, respectively, their characteristic impedances. In the lter 5 it has been assumed that the voltage requirement can be met with a single shunt line section I6. However, if greater spacing between inner and outer conductors is required, two or more parallel-connected shunt branches may be used, as in the lter 4, in which case Equations 12 and 13 Will be modified by the inclusion -of the factor n as in Equations 3 and 4.

Neglecting the end shunt capacitances CD, CD, as was done in connection with the circuit of Fig." 2, the design formulasfor the circuit of Fig. 3 'are as'rfollows:

Z ,Lpg-1222 (14.)y

Zo(f222-f122) l LE- 47rf122f22 (15) mitofmfif) 16) The iirsttransmission band of the filter 5 is usedand it is located Within one of the attenuation bands of the filter 4. Preferably the third attenuation band is chosen, th'at is, the one between the upper cut-off f21 of the second transmission band and the lower cut-off fn" of the third transmission band. If the second attenuation band, between the frequencies .121 and fn', is chosen the sum of the lengths D and E may exceed A, resulting in an inconvenient mechanical structure.

The lower cut-off i12 of the lter 5 is, therefore, placed at a frequency interval above ,zi' and the upper cut-01T fzz at an interval below fn. lThese intervals are preferably approximately equal and each should be at least as large as h'alf of the band width fzi-n of the lter 4 to insure that the lter 4 will have a low enough image impedance over the band of the filter 5 for successful operation of the two filters in series. In the example shown the cut-offs fm and fzz are located respectively, at the frequencies 805 and 1087 megacycles, giving a midband frequency of 935 megacycles. Since the third attenuation band of the lter 4 extends between 751 and 1142 megacycles, fifi is 54 megacycles above fzi and fzs is 55 megacycles below fn". These intervals are larger than half of the megacycle band width of the filter 4. The broken line curve of Fig. 4 shows the characteristic of the lter 5.

Using Equations 8 to 16 and the same design procedure outlined above in connection with the filter 4, each of the series line sections I4 and I5 of the iilter 5 of the example will have a length D of 4.72 centimeters and a characteristie impedance of 46.6 ohms and the shunt line section I6 a length E of 8.02 centimeters and a characteristic impedance of 13.94 ohms. From Equation 9, it is found that for the series branches I4 and I5 the ratio of the inner diameter of the outer conductor to the diameter of the inner conductor will be 2.17 and for the shunt branch I6 this ratio will be 1.262. Since the conductor I2 with an outer diameter of 1.270 centimeters is the inner conductor of line section I4, the outer conductor 30 will have an inside diameter of 2.75 centimeters. The other series line section I5 will also have an inner conductor 3l with' a diameter of 1.270 centimeters and an outer conductor 3'2 with an inner diameter of 2.75 centimeters. The diameter of the outer conductor 33 of the shunt line section I6 may conveniently be vmade the same as that of the series section I4, giving a diameter of 2.18 centimeters for the inner conductor 34. The required diameter for the inner conductor 34 may be provided by building up the outer diameter of the conductor I2 by adding material. Or, if desired, the inner conductor 34 may be in the form of a hollow cylinder with an annular plate at the end 35 which' ts over the conductor I2. In order to prevent the formation of a corona discharge it is Well to round on the end of the inner conductor 34 as shown at 36. In the line sections I4 andJE the inner' andi outer conductors will have aiseparation of 0.74v

and in the line section I6 a separation of 0.28, more than sufficient toY withstand the peak voltage assumed. Y

The formulas involving the lengths of the coaxial line sections given herein are based upon the assumption th'at the concentric outer conductor will extend for the full length of the section. As is apparent in Fig. 1, however, when one branch, such as I5, is connected at a right angle to another branch, such as III, at least a portion of the outer wall will be missing at the connected ends of` the sections. In order to compensate for this condition the lengths of the line sections may have to be increased somewh'at.V This factor is of more importance in lters operating at the higher frequencies. of side branches/such as 8, 9 and I5 it has been found that amore nearly correct result will be obtained if the length is measured from the outer conductor, as` shown by the dimensions B and D. n v

What is claimed is:

1. In combination, two Wave filters connected in series atone end, each of said filters including a section ofY transmission line or" the type comprising a cylindrical outer conductor and an inner conductor coaxial therewith, andthe inner conductor of one of said sections serving also as the outer conductor of the other of said sections.

2. The combination in accordance with claim 1 in which said sections are located at the seriesconnected ends of said filters.

3. The combination in accordance with claim 1 in which one of said lters includes a second section of coaxial transmission line, said second section being arranged in axial alignment Ywith said first-mentioned section rin saidVV one iilter, and concentrically with respect to said section insaid other lter.

4. The combination in accordance with claiml in whichl one of said lters includes two additional sections of coaxial transmission line of equal length connected in parallel with each other at the same point in said one iilter.

k. YThe combination in accordance with claim 1 in which one of said lters includes a second section of coaxial transmission line, saidV second Section being arranged in axialV alignment with said first-mentioned section in said one'ilter and" concentrically with respect to said section in said other lter and being short-circuited at one end.

In the case 6. The combinationjinfaccordance with claim 1 in which one of said filters includesv a second section and a third section of coaxial transmis- 7. In combination, two Wave filters connected in` series at one end, each of said filters including a plurality of sections oi coaxiall transmission line, I two of Saidy sections in one of said filters beingV arranged in axial alignment with. each other concentrically about one of saidsections in the other of said i'llters, and one of said two sections in said one lter being short-circuited atone end.

8. The combination in accordance with claim 7 in which one of said filters includes two sections of coaxial transmission line of equal length con-v nected in parallel with each other at4 the same point.

9. The combination in accordance with claim'7 in which one of said iilters includes two sections of coaxial transmission line of equal length and the same characteristic impedance connected in parallel with each other at the same point.

10. The combination in accordance with claim 7 in which said one filter includes a third section of coaxial transmission line connectedat the j unctionY of said two sections in said'one filter.

11.` The combination in accordance with claim v7 in which said one lter includes .a third section of coaxial transmission line connected at av right angle at the junction of said tWo sections in said onefilter. Y

Y WARREN P. MASON. Y

REFERENCES CITED The following references are of `record in the le of. this patent: Y

UNITED STATES PATENTS Mason May 26, 1942 Y 

